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GEOSTATS: covariance VS. Variogram.

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  • Yaron Felus
    Hi list, I was wandering about section 5.3 of the Geostatistics FAQ. ( http://curie.ei.jrc.it/faq/sc_general.html ) Which says that it is sometimes
    Message 1 of 2 , Jun 11 10:22 PM
      Hi list,

      I was wandering about section 5.3 of the Geostatistics FAQ.
      ( http://curie.ei.jrc.it/faq/sc_general.html )
      Which says that it is sometimes advantageous to use the covariance over the
      Variogram.

      I have a few references that prove the opposite of this fact for example:

      Cressie A.C. Noel. and Grondona O. Martin (1992); A comparison of Variogram
      Estimation with Covariogram Estimation, In The art of statistical Science
      Edited by K.V. Mardia Jhon pp:191-208, Wiley & Sons Ltd.

      and also in

      Cressie N.A.C. (1993) Statistics for spatial data. New York Wiley.

      Cressie and Grondona (1992) proves that variogram estimation is to be
      preferred to covariogram estimation; the main reasons for that are:
      1. In the Kriging process where we estimate the mean of the process and then
      predict the random process both the variogram estimator and covariogram
      estimator are biased. However the variogram bias is of smaller order.
      2. If our data has trend contamination then it has �disastrous effect� on
      attempts to estimate the covariogram while on the variogram it has a �small
      upward shift�.

      Does anybody have a reference (or reason) which supports this statement that
      the covariance has any advantage over the Variogram ?

      Thank you in advance.

      Yaron A. Felus.
      Research associate.
      The Ohio-State University.
      Department of Civil and Environmental Engineering and Geodetic.
      ________________________________________________________________________
      Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com

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    • Yaron Felus
      Hi all To all of you asking for summery of answers, I am out of the country right now and will be back after ISPRS congress 7/23, sorry for the delay, I
      Message 2 of 2 , Jun 26 1:52 PM
        Hi all

        To all of you asking for summery of answers, I am out of the country right
        now and will be back after ISPRS congress 7/23, sorry for the delay, I
        promise to post all the answers and my interpretation when I come back.

        Thanks.

        Yaron A. Felus.
        Research associate.
        The Ohio-State University.
        Department of Civil and Environmental Engineering and Geodetic.

        >I was wandering about section 5.3 of the Geostatistics FAQ.
        >( http://curie.ei.jrc.it/faq/sc_general.html )
        >Which says that it is sometimes advantageous to use the covariance over the
        >Variogram.
        >
        >I have a few references that prove the opposite of this fact for example:
        >
        >Cressie A.C. Noel. and Grondona O. Martin (1992); A comparison of Variogram
        >Estimation with Covariogram Estimation, In The art of statistical Science
        >Edited by K.V. Mardia Jhon pp:191-208, Wiley & Sons Ltd.
        >
        >and also in
        >
        >Cressie N.A.C. (1993) Statistics for spatial data. New York Wiley.
        >
        >Cressie and Grondona (1992) proves that variogram estimation is to be
        >preferred to covariogram estimation; the main reasons for that are:
        >1. In the Kriging process where we estimate the mean of the process and
        >then predict the random process both the variogram estimator and
        >covariogram estimator are biased. However the variogram bias is of smaller
        >order.
        >2. If our data has trend contamination then it has �disastrous effect� on
        >attempts to estimate the covariogram while on the variogram it has a �small
        >upward shift�.
        >
        >Does anybody have a reference (or reason) which supports this statement
        >that the covariance has any advantage over the Variogram ?
        >

        ________________________________________________________________________
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